reserve X, Y for non empty set;
reserve X for non empty set;
reserve R for RMembership_Func of X,X;

theorem Th25:
  1 iter R = R
proof
  consider F being sequence of Funcs([:X,X:],[. 0,1 .]) such that
A1: 1 iter R = F.1 & F.0 = Imf(X,X) and
A2: for k being Nat ex Q being RMembership_Func of X,X st F.k
  = Q & F.(k + 1) = Q (#) R by Def9;
  ex Q being RMembership_Func of X,X st F.0 = Q & F.(0 + 1 ) = Q (#) R by A2;
  hence thesis by A1,Th22;
end;
